$2$

$[$GT R$-1\mathrm{.}7]$

Order the following list of functions by the $O()$ notation, from smallest to largest. Group to$-$

gether those functions that are in $)$ of one another.

Note: If no base is given, assume that $logn$ is $lo{g}_{2}n.$

Hint: When in doubt about two functions $f(n)$ and $g(n),$ consider $logf(n)$ and $logg(n)$ or

$2^{f(n)}$ and $2^{g(n)}.$